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(CNN) – As he stood on the floating Apollo 11 capsule, Navy SEAL John Wolfram was very aware that the safety of the first men to walk on the moon was in his hands. The whole world was watching.

Amazing circumstances – for a guy just two years out of high school.

It was July 24, 1969 – four days after the historic landing – and millions were anxious to know whether the astronauts had survived their fiery fall into the Pacific about a thousand miles off Hawaii. Minutes before he stepped onto the tiny capsule, it had been plummeting from space into the atmosphere at thousands of miles per hour. Parts of the spacecraft’s shell were blackened. Wolfram could see steam still rising from it.

“I looked in the hatch window to see if the astronauts were OK,” recalls Wolfram. “They smiled and gave me a thumbs up. Being the first to look them in the eye and see that they’re OK – it’s quite a rush.”

On this 43rd anniversary of the well-known mission, here’s an Apollo 11 story that’s told less often.

It’s the story of a handpicked four-man team of tough Navy SEALs who played a key role in what may be mankind’s greatest technological achievement.

“The splashdown of Apollo 11 represented that very moment when President (John F.) Kennedy’s national goal of placing a man on the moon before the decade was out and returning him safely to Earth was finally accomplished,” says Scott Carmichael, author of “Moon Men Return.”

Because the task was incredibly physically demanding, the Navy had picked its strongest swimmers – elite graduates of its SEAL training school, known to be among the toughest of its kind in the world. They had trained for months and served on recovery teams for previous Apollo moonshots.

The mission: stabilize and secure the spacecraft, decontaminate the astronauts and get them safely aboard a hovering helicopter bound for the aircraft carrier USS Hornet.

Before Wolfram could ever step onto the spacecraft, he first had to catch it. From a chopper hanging low over the site, he jumped into the cold sea. Then he had to lasso a high-tech bucking bronco.

The fact that Wolfram was able to attach an underwater parachute – called a sea anchor– to stop the drifting “bobbing, 12,000-pound spinning behemoth,” was an almost super-human accomplishment, says Carmichael. “If that thing hits you in the head, you’re done.”

The spacecraft was drifting away from Wolfram, pitching up and down.

“You only get one chance at this. The capsule was moving so fast in a high-gust situation that if a swimmer misses that hand hold, he’ll never catch up to it,” says Carmichael. Wolfram had very little time to grab a tiny recessed hand-hold on the vessel – and when he did, it pulled him out of the water like a fish on a hook. “He held on and managed to get that sea anchor attached.”

Joined by lead frogman Wes Chesser and teammate Mike Mallory, the trio then struggled against 12-foot-high waves and 28-mph winds to attach a 200-pound inflatable floatation ring around the spacecraft. “We were the muscle guys of the outfit,” jokes Mallory, 66, who now works with utility control systems in Hartland, Michigan.

NASA officials were impressed with how quickly they wrapped the ring around the vessel. “Wolfram and I were very strong swimmers, so we muscled that ring around there,” Mallory says. According to Carmichael, Mallory’s physical power made him a “horse” when it came to swimming in the open water of the Pacific. And Chesser “was just unflappable,” says Carmichael.

“All hell could be breaking loose and Wes just had that capacity to calmly look at something and figure out what needed to be done.”

The team attached inflatable rafts to the capsule and overall mission leader Clancy Hatleberg helped astronauts Neil Armstrong, Michael Collins and Buzz Aldrin out of the capsule – unsure if they would be able to stay on their feet after days in zero gravity.

The Apollo crew and the frogmen put on special suits and masks – called biological isolation garments – to protect them against “lunar pathogens” – possible biological threats the astronauts may have unknowingly brought back from the moon.

There were a few minor glitches. The masks made it was difficult to communicate, forcing the men at times to use hand signals. At one point the masks’ goggles began to steam up. For a few minutes, they had trouble getting the capsule hatch to lock shut.

“It would have compromised the floating integrity of the spacecraft to leave the hatch open,” says Chesser, remembering how an open hatch led to the flooding and sinking of astronaut Gus Grissom’s space capsule after splashdown in 1961.

One-by-one, Hatleberg helped the astronauts into a basket-like carriage called a Billy-Pugh net before they were hoisted into a Navy chopper for the ride to the USS Hornet.

The space race “was an extremely exciting time for our country,” says Chesser, the kind of excitement that has since gone away. Now with the end of NASA’s space shuttle program, U.S. space technology and operations are shifting toward private industry and commercial space ventures.

Government-run and privately run space-flight have their own advantages, says Chesser, 67, now a retired defense contractor. “But the space program is of strategic importance. In time of war – or needing to defend ourselves – it seems like it should be under the cognizance of NASA and the (military) services.”

After making Apollo 11 history, and serving two tours in the Vietnam War, Wolfram’s life changed forever in 1971, when he attended a church revival. He’s now an ordained minister who serves much of each year as a missionary in Southeast Asia.

He and Chesser have visited Washington’s Smithsonian National Air and Space Museum which is now home to the Apollo 11 capsule. “I loved being a Navy frogman,” recalls Wolfram, now 63, who detailed his adventure in a memoir, “Splashdown.”

For Chesser, seeing the spacecraft again put the mission in a new light.

“What we did seemed so easy back then because we trained so hard and were in good shape, but years later I realized how physically demanding that whole process was,” Chesser says. “To think about having to do that mission today, I probably would half drown.”

The Apollo crew summed it up 43 years ago on live TV aboard the USS Hornet.

President Nixon asked the astronauts jokingly if their splashdown recovery was the most difficult part of their mission.

Neil Armstrong replied with a smile, “It was one of the hardest parts.”